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The purpose of this paper is the development of a new numerical method for the calculation of the air-gap magnetic flux harmonics in synchronous machines with permanent magnet (PM) excitation. The harmonic analysis results are used as input data for the eddy-current loss calculation and for the rotor heating evaluation.

The method is based on the finite element analysis (FEA). The model takes into account toothed stator design, rotor asymmetrical magnetic reluctance and saturation. At first, a series of static DC magnetic (magnetostatic) simulations is run. Each problem corresponds to specific rotor position and the momentary stator winding currents. The Fourier analysis performed for each problem yields the harmonic spectrum variation in time. Then, a series of AC magnetic (time-harmonic) simulations is run. Each problem corresponds to a specific harmonic. The result is the eddy-current losses distribution. After total loss is calculated, the heat transfer analysis is conducted.

The analysis reveals that 90 per cent of losses are located in the sleeve that holds PMs together. Rotor eccentricity brings even harmonics of low magnitude that have little impact on heating.

In general, the study requires transient electromagnetic analysis with motion. The purposed method allows to simplify the problem. The method is based on static and quasi-static (time-harmonic) problems simulation. It is fast and highly automated. The method allows simultaneous taking into account of tooth-order harmonics, stator winding harmonics and eccentricity for heating calculation.